If you post photos, especially of the receiver top and sides, you might get more info confirming which model it is.
Assuming it is a Model 1860, I don't see a direct match for that serial number in the records I have--it falls in the range of rifles issued to the 9th Michigan Volunteer Cavalry, but not far in number from known Ohio Sharpshooter rifles. If an M1860 rifle, it was likely manufactured in 1863.
There is scant specific serial number information about the other models.